Axion-Like Particles and the Higgs Decays h \rightarrow PZ and h \rightarrow P \ell^+ \ell^-

Axion-like particles (ALPs) are often defined as relatively light pseudoscalar particles and appear in many extensions of the Standard Model. Taking into account constraints on the free parameters from existing searches and explaining the g-2 deviation, we consider the contributions of ALPs with mass in the range of 1.5 GeV\, < m_a < m_h-m_Z to the exclusive Higgs decays h \rightarrow PZ and h \rightarrow P\ell^+ \ell^- with P being the pseudoscalar mesons \pi^0, \eta, \eta', \eta_c and \eta_b in a model-independent approach. We find that, in most of the parameter space range, the contributions of ALP to these decay processes are very small, while in the case of the ALP mass m_a approximately equaling the meson mass m_P, the contributions are significantly large.